Vapor pressure example | Chemistry | Khan Academy

Khan Academy
18 Oct 201016:02
EducationalLearning
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TLDRIn this educational transcript, the concept of vapor pressure is explored through an experiment involving 2 liters of water in a sealed room. The Ideal Gas Law is applied to determine that only 983 milliliters of water will evaporate at 25 degrees Celsius, demonstrating that not all water will evaporate due to equilibrium between evaporation and condensation.

Takeaways
  • 📚 The exercise is from the book 'Chemistry and Chemical Reactivity' by Kotz, Treichel, Townsend, and others.
  • 💧 The scenario involves 2 liters of water placed in an open container in a sealed room with a volume of 4.25 x 10^4 liters.
  • 🌡 The temperature given is 25 degrees Celsius, where the density of water is 0.997 g/mL and its vapor pressure is 23.8 mmHg.
  • 🔍 The concept of vapor pressure is explained as the equilibrium pressure between the liquid and gas phases of a substance.
  • 🔄 Vapor pressure is the point where the rate of evaporation equals the rate of condensation of water molecules.
  • 📐 The Ideal Gas Law (PV = nRT) is introduced as the key formula to solve the problem, relating pressure, volume, number of moles, and temperature.
  • ⚖️ The vapor pressure is converted to atmospheres for consistency with the units of the universal gas constant.
  • 🔢 The calculation involves using the Ideal Gas Law to find the number of moles of water vapor at equilibrium in the room.
  • 🧪 The molar mass of water is used to convert moles of water vapor to grams, which then helps in determining the volume of water evaporated.
  • 📉 It is concluded that only 983 milliliters of water will evaporate to reach the equilibrium vapor pressure at 25 degrees Celsius.
  • 🚫 The final answer to the question is that not all of the water will evaporate, as only a little less than half of the 2 liters will do so.
Q & A

  • What is the main topic of the exercise described in the script?

    -The main topic of the exercise is to determine whether all of the water placed in an open container in a room will evaporate at 25 degrees Celsius, using principles of chemistry and the Ideal Gas Law.

  • What is the volume of the room in which the water is placed?

    -The volume of the room is 4.25 times 10 to the fourth liters.

  • What is the density of water at 25 degrees Celsius as mentioned in the script?

    -The density of water at 25 degrees Celsius is 0.997 grams per milliliter.

  • What is the vapor pressure of water at 25 degrees Celsius according to the script?

    -The vapor pressure of water at 25 degrees Celsius is 23.8 millimeters of mercury.

  • What is the significance of vapor pressure in this context?

    -Vapor pressure is the pressure at which the liquid and vapor states of a substance are in equilibrium. It is a key factor in determining how much water will evaporate in the room.

  • What law or formula is used to solve this problem?

    -The Ideal Gas Law is used to solve this problem, which relates pressure, volume, number of moles, and temperature.

  • What is the role of the universal gas constant in the Ideal Gas Law?

    -The universal gas constant (R) is a proportionality constant that relates the pressure, volume, and temperature of a gas to the number of moles of the gas.

  • How is the vapor pressure converted to atmospheres in the script?

    -The vapor pressure is converted to atmospheres by dividing 23.8 millimeters of mercury by 760, which gives approximately 0.0313 atmospheres.

  • What is the molar mass of water used in the calculations?

    -The molar mass of water used in the calculations is approximately 18.01 grams per mole.

  • How many grams of water need to evaporate to reach the equilibrium vapor pressure?

    -980 grams of water need to evaporate to reach the equilibrium vapor pressure.

  • What is the final conclusion about the evaporation of water at 25 degrees Celsius in the room?

    -The conclusion is that not all of the water will evaporate at 25 degrees Celsius; only a little bit less than half of it will evaporate to reach the equilibrium vapor pressure.

Outlines
00:00
💧 Introduction to Water Evaporation and Vapor Pressure

This paragraph introduces the problem of water evaporation in a sealed room from a chemistry textbook. It explains the conditions: 2 liters of water in a 4.25 x 10^4 liters room at 25°C, with the density and vapor pressure of water provided. The key concept introduced is vapor pressure, which is the pressure at equilibrium between the liquid and gas phases of a substance. The explanation includes a review of what vapor pressure is, using the kinetic energy of water molecules as an analogy to explain the process of evaporation and the establishment of equilibrium pressure.

05:01
🔍 Delving into the Ideal Gas Law for Vapor Pressure Calculation

The speaker transitions into applying the Ideal Gas Law to calculate the number of water molecules that need to evaporate to reach the given vapor pressure. The law relates pressure, volume, the number of moles, and temperature, which are all variables in this scenario. The paragraph emphasizes the importance of using the correct units and constants, converting the vapor pressure from millimeters of mercury to atmospheres, and setting up the equation to solve for the number of moles of water vapor that would be present at equilibrium in the room.

10:02
📚 Calculation of Water Moles and Conversion to Grams

This section details the mathematical process of using the Ideal Gas Law to determine the moles of water vapor at equilibrium. The calculation involves converting the given vapor pressure to atmospheres, using the room's volume, the universal gas constant, and the temperature in kelvin. The result is 54.4 moles of water vapor. The speaker then converts moles to grams using the molar mass of water, yielding approximately 980 grams of water that need to evaporate to achieve the stated vapor pressure.

15:08
🌡 Final Analysis of Evaporation at 25 Degrees Celsius

The final paragraph concludes the problem by calculating the volume of water that will evaporate, which is less than half of the initially placed 2 liters. The speaker confirms that not all the water will evaporate at 25°C in a sealed room, as only 983 milliliters are needed to reach the equilibrium vapor pressure. This confirms the understanding that beyond this point, the rate of evaporation equals the rate of condensation, maintaining a constant pressure and preventing further evaporation.

Mindmap
Keywords
💡Evaporation
Evaporation is the process by which a substance in its liquid state changes into a vapor under the influence of heat or as a result of any other factors. In the video, the concept is central to understanding the problem of water evaporating in a sealed room. The script discusses how water molecules at 25 degrees Celsius gain enough kinetic energy to escape the liquid state and enter the gaseous state, which is a key part of the vapor pressure equilibrium.
💡Vapor Pressure
Vapor pressure is the pressure exerted by a vapor in equilibrium with its condensed phases at a given temperature in a closed system. It is a critical concept in the script, as it is used to determine the amount of water that can evaporate in the room. The script explains that at 25 degrees Celsius, the vapor pressure of water is 23.8 millimeters of mercury, which is a key piece of data for solving the problem.
💡Density
Density is defined as the mass per unit volume of a substance. In the context of the video, the density of water at 25 degrees Celsius is given as 0.997 grams per milliliter. This information is crucial for calculating the volume of water that would correspond to a certain mass of water vapor, as it helps to relate the mass of the evaporated water to its volume.
💡Ideal Gas Law
The Ideal Gas Law is a fundamental principle in physical chemistry that relates the pressure, volume, temperature, and the number of moles of an ideal gas. The script uses this law (PV = nRT) to calculate the number of moles of water vapor needed to achieve the given vapor pressure at a specific temperature and volume. It is a central formula for solving the problem presented in the video.
💡Molar Mass
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. The script mentions the molar mass of water, which is approximately 18.01 grams per mole, to convert the number of moles of water vapor to its mass in grams. This is essential for determining how much water can evaporate to reach the equilibrium vapor pressure.
💡Kinetic Energy
Kinetic energy is the energy that a body possesses due to its motion. In the video, the concept is used to explain how water molecules at 25 degrees Celsius have enough kinetic energy to overcome intermolecular forces and escape into the vapor phase. This is a fundamental aspect of the evaporation process described.
💡Hydrogen Bonds
Hydrogen bonds are a type of chemical bond that occurs between a hydrogen atom covalently bonded to a highly electronegative atom and a neighboring electronegative atom. The script refers to hydrogen bonds as one of the forces that keep liquid water in its liquid state, which must be overcome for evaporation to occur.
💡Equilibrium
Equilibrium in chemistry refers to a state in which two opposing processes occur at the same rate, so no net change in the system is observed. In the context of the video, the equilibrium is reached when the rate of water molecules evaporating equals the rate of water vapor condensing back into the liquid state, which is determined by the vapor pressure.
💡Moles
Moles are a unit of measurement used in chemistry to express amounts of a chemical substance, based on the number of entities present. The script uses the concept of moles to calculate the amount of water vapor needed to achieve the vapor pressure in the room, as well as to convert this amount into grams using the molar mass of water.
💡Milliliters
Milliliters are a unit of volume measurement in the metric system, where one milliliter is equal to one cubic centimeter. The script uses milliliters to express the volume of water in the container and to calculate the volume of water that will evaporate based on its density and the mass of the evaporated water.
Highlights

The exercise is from chapter 12 of the Kotz, Treichel, Townsend, and Chemistry and Chemical Reactivity book.

The problem involves calculating whether all 2 liters of water will evaporate in a sealed room at 25 degrees Celsius.

The room's volume is given as 4.25 x 10^4 liters, a key parameter for the calculation.

At 25 degrees Celsius, water's density is 0.997 grams per milliliter and its vapor pressure is 23.8 millimeters of mercury.

Vapor pressure is the key to solving the problem, representing the equilibrium between liquid and gas phases.

A review of vapor pressure explains how water molecules escape and return to the liquid state at equilibrium.

The Ideal Gas Law (PV=nRT) is introduced as the formula to relate pressure, volume, number of moles, and temperature.

The importance of using the correct units for the universal gas constant is emphasized for accurate calculations.

Conversion of vapor pressure from millimeters of mercury to atmospheres is necessary for the Ideal Gas Law calculation.

The calculation involves dividing the product of vapor pressure and room volume by the gas constant and temperature.

Temperature must be converted to Kelvin (298K) for the calculation, which is a critical step in using the Ideal Gas Law.

The calculated number of moles of water vapor (54.4 moles) represents the equilibrium state in the room.

The molar mass of water (18.01 g/mol) is used to convert moles to grams for understanding the mass of evaporated water.

The density of water at 25 degrees Celsius allows for the conversion of grams to milliliters to find the volume of evaporated water.

Only 983 milliliters of the 2 liters of water will evaporate to reach the equilibrium vapor pressure at 25 degrees Celsius.

The conclusion is that not all of the water will evaporate, contrary to the initial assumption, only a little less than half will.

The exercise demonstrates the application of the Ideal Gas Law in a real-world scenario involving evaporation and vapor pressure.

Transcripts

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Chemistry ExerciseEvaporation ProcessVapor PressureIdeal Gas LawThermodynamicsHydrogen BondsWater MoleculesEquilibrium StateKinetic EnergyScience Education